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Lecture Series

Workshop on Topology:  Identifying Order in Complex Systems


Date: Saturday, October 18, 2014
Location:  Hill Center – Room 705
Busch Campus, Rutgers University
Piscataway, NJ 08854

Speaker: Gareth Alexander, University of Warwick

Title:  Topological Order: Umbilics in Chiral Liquid Crystals

Time:  9:30am – 10:30am

Abstract:  Recent experimental advances have opened the door to laboratory realisations of a large range of complex textures with distinctive topological properties, including knots, skyrmions and "Hopf fibrations" in optics, fluids, helical magnets and liquid crystals. We will show how the order in these materials can be described in terms of certain naturally defined vector bundles, whose generic zeros we dub umbilics and which manifest themselves in magnetic skyrmions and the lambda defects of cholesteric liquid crystals. Focussing on the examples from liquid crystals we will explain how the geometry of these vector bundles captures the geometry of the material, while their characteristic classes convey the topology.

Speaker:  Ronald Coifman, Yale University

Title:  Geometries of Sensor Outputs, Inference, Fusion and Information Processing

Time:  9:30am – 10:30am

Abstract:  Our goal is to describe extensions of the main tools of signal processing, denoising feature extraction, prediction, regression, to deal with more general data sources such as heterogeneous nonlinearly correlated multisensor inputs, questionnaires, text and other digital documents. In particular we introduce functional geometric dualities between data attributes and datasets.

We describe general methodologies based on various diffusion geometries for building empirical inferential structures on digital data (such as collaborative filters or recommendation engines ). We indicate natural geometries for fusing information through the combination of several inferential structures. Examples covering questionnaire data analysis, multisensor image processing and data fusion will be described.

Speaker :  Elizabeth Munch, SUNY Albany

Title:  Towards Predicting and Preventing Machine Chatter Using Persistent Homology

Time:  1:30am – 2:30am

Speaker :  Frederick Chazal, INRIA

Title:  A Few Statistical Properties of Topological Information Inferred from Data

Time:  3:00am – 4:00am

Speaker:  Yasuaki Hiraoka, Kyushu University

Title:  Topological Data Analysis on Amorphous Structure

Time:  4:30pm – 5:30pm

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530